What is the degree of the homogeneous function √(x^2 + y^2)?

Homogeneous & Linear Differential Equations · Question 11 of 120

Question 11

MediumOriginal question

What is the degree of the homogeneous function $\sqrt{x^{2} + y^{2}}$ ?

0

Correct answerYour answer

\frac{1}{2}

Correct answerYour answer

1

Correct answerYour answer

2

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Replace $x, y$ by $\lambda x, \lambda y$ and see which power of $\lambda$ comes out.
It comes out as $\lambda^{1}$ , so the degree is 1.

Worth noting

2 is the degree under the root; the square root halves it.

Ten questions from Homogeneous & Linear Differential Equations, at your own pace.

Ten questions from Homogeneous & Linear Differential Equations, at your own pace.